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| A MUTI-RESOLUTION TIMOSHENKO BEAM ELEMENT FORMULATION |
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Abstract A multi-resolution beam element with bending based on the Timoshenko theory is proposed. The multi-resolution analysis (MRA) performance of the element is formulated out of a nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the interval [0,1] of node shape functions extended from the traditional interval [0,1] to the [-1,1]. The MRA property enables this one proposed element to be re-meshed freely just by means of adjusting its resolution level, thus modulating its analysis accuracy accordingly. The extended shape functions make all the sub-elements connect together at the nodes as a whole as the initial proposed element in the re-meshing process, that is, the stiffness, the mass matrices and the equivalent node loading vectors can be obtained automatically without being reassembled artificially，thus, being seen as a technical secret for assembling artificially of node-related items in global matrix formation by the conventional. In addition, the proposed beam element can deal with the boundary conditions conveniently just as a conventional Timoshenko beam element does. In this sense, the MRA concept is fulfilled for the first time for a Timoshenko beam element and the mathematic essence, a nesting displacement subspace sequence, is found for meshing of beam structure in this paper.
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Received: 26 November 2012
Published: 28 February 2014
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| [1] |
. Stability analysis of spatial beam based on corotational formulation[J]. , 2014, 35(1): 49-56. |
| [2] |
. Large Deflection Analysis of a Saturated Poroelastic Timoshenko Beam[J]. , 2012, 33(1): 0-111. |
| [3] |
. Static Response of Timoshenko Sandwich Beam Made of Functionally Graded Materials under Thermal Loads[J]. , 2011, 32(5): 483-492. |
| [4] |
. Quasi-static Bending of Saturated Poroelastic Timoshenko Cantilever Beam[J]. , 2011, 32(4): 382-389. |
| [5] |
. Mathematical Model for Dynamics of Incompressible Saturated Poroelastic Timoshenko Beam[J]. , 2010, 31(4): 397-405. |
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2014, Vol. 35 
